Select Goal &
City
Select Goal
Explore
Question:
In the x-y plane, a vector is given by
\(\overrightarrow𝐹 (𝑥, 𝑦) = \frac{−𝑦𝑥̂ + 𝑥𝑦̂}{𝑥^ 2 + 𝑦^2} . \)
The magnitude of the flux of \(\overrightarrow∇ ×\overrightarrow 𝐹\) , through a circular loop of radius 2, centered at the origin, is:
In the x-y plane, a vector is given by
\(\overrightarrow𝐹 (𝑥, 𝑦) = \frac{−𝑦𝑥̂ + 𝑥𝑦̂}{𝑥^ 2 + 𝑦^2} . \)
The magnitude of the flux of \(\overrightarrow∇ ×\overrightarrow 𝐹\) , through a circular loop of radius 2, centered at the origin, is:
\(\overrightarrow𝐹 (𝑥, 𝑦) = \frac{−𝑦𝑥̂ + 𝑥𝑦̂}{𝑥^ 2 + 𝑦^2} . \)
The magnitude of the flux of \(\overrightarrow∇ ×\overrightarrow 𝐹\) , through a circular loop of radius 2, centered at the origin, is:
Updated On: Oct 1, 2024
- π
- 2π
- 4π
- 0
Hide Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
The correct option is (B): 2π
Was this answer helpful?
0
0
Top Questions on Mathematical Methods
- The value of the line integral for the vector,
\(\overrightarrow𝑣=2𝑥̂ +𝑦𝑧 ^2𝑦̂ +(3𝑦+𝑧 ^2 )𝑧̂ \)
along the closed path OABO (as shown in the figure) is:
(Path AB is the arc of a circle of unit radius)- IIT JAM - 2024
- Physics
- Mathematical Methods
- A vector field is expressed in the cylindrical coordinate system (s, ϕ, z) as,
\(\overrightarrow𝐹=\frac{𝐴}{𝑠} 𝑠̂+ \frac{𝐵}{𝑠} 𝑧̂. \)
If this field represents an electrostatic field, then the possible values of A and B, respectively, are:- IIT JAM - 2024
- Physics
- Mathematical Methods
- Which of the following matrices is Hermitian as well as unitary?
- IIT JAM - 2024
- Physics
- Mathematical Methods
- The sum of three binary numbers, 10110.10, 11010.01, and 10101.11, in decimal system is:
- IIT JAM - 2024
- Physics
- Mathematical Methods
- The roots of the polynomial, 𝑓(𝑧)=𝑧 4-8𝑧 3+27𝑧 2-38𝑧+26, are 𝑧1, 𝑧2, 𝑧3,& 𝑧4, where 𝑧 is a complex variable. Which of the following statements is correct?
- IIT JAM - 2024
- Physics
- Mathematical Methods
View More Questions
Questions Asked in IIT JAM exam
- One mole of an ideal monoatomic gas is heated in a closed container, first from 273K to 303K, and then from 303K to 373K. The net change in the entropy is ______R. (Rounded off to two decimal places) (R is the ideal gas constant)
- IIT JAM - 2024
- Modern Physics
- In a Newton’s rings experiment (using light of free space wavelength 580nm), there is an air gap of height d between the glass plate and a plano-convex lens (see figure). The central fringe is observed to be bright.
The least possible value of d (in nm) is:- IIT JAM - 2024
- Modern Physics
- If the electric field of an electromagnetic wave is given by,
𝐸⃗ = (4𝑥̂ + 3𝑦̂)𝑒 𝑖(𝜔𝑡+𝑎𝑥−600𝑦)
then the value of a is: (all values are in the SI units)- IIT JAM - 2024
- Electricity
- If two traveling waves, given by
𝑦1=𝐴0 sin(α𝑘𝑥 -𝜔𝑡) and 𝑦2=𝐴0 sin(α𝑘𝑥 − β𝜔𝑡)
are superposed, which of the following statements is correct?- IIT JAM - 2024
- Oscillations
- A particle moving along the x-axis approaches 𝑥=0 from 𝑥 =−∞ with a total energy E. It is subjected to a potential 𝑉(𝑥). For time 𝑡→∞, the probability density P(x) of the particle is schematically shown in the figure.
The correct option for the potential 𝑉(𝑥) is:- IIT JAM - 2024
- Oscillations
View More Questions
SUBSCRIBE TO OUR NEWS LETTER
COLLEGE NOTIFICATIONSEXAM NOTIFICATIONSNEWS UPDATES
Download the Collegedunia app on 
© 2024 Collegedunia Web Pvt. Ltd. All Rights Reserved